Question

a builder makes drainpipes that drop 1 cm over a horizontal distance of 30cm to provent clogs a certain drainpipe needs to cover a horizontal distance of 700cm whats is the lenght of the drainpipe? round your answer to the nearest tenth of a centimeter

Answer 1

• 700.4cm

Step-by-step explanation:

The ratio of the vertical drop to the horizontal distance covered is 1 cm / 30 cm.

If you draw the drainpipe as a straight line, the angle of inclination, β, will be such that:

• tan(β) = 1/30

Then, β = arctan(1/30) = 1.90915º

Now you can relate the length of the drainpipe with the angle and the horizontal distance with the trigonometric ratio cosine:

• cos(β) = adjacent leg / hypotenuse

• cos(β) = horizontal distance / length of the drainpipe

• length of the drainpipe = 700cm / cos(.190915º)

• length of the drainpipe = 700.4 cm ← answer